METAFRACTALS3D Fractals & Bicomplex Dynamics
Articles

Articles & academic work

Twenty-five years of bicomplex and multicomplex dynamics, from the first generalized Mandelbrot set for bicomplex numbers (2000) to the algebraic foundation of the Mandelbulb (2023) and Claude's Cat (2026).

Academic Work

  1. D. Rochon, Sur une généralisation des nombres complexes: les tétranombres, Master's Thesis, Université de Montéal, 1997.
  2. D. Rochon, Dynamique bicomplexe et théorème de Bloch pour fonctions hyperholomorphes, Doctoral Thesis, Université de Montréal, 2001.

Poetry

  1. M. Gorski & D. Rochon, L'ÉVEIL DU GRAND JOUR : Les chants tantriques de la théurgie fractale, ISBN 978-2-9817658-6-4, Éditions de l'Exil, 2020.

Synthetic Intelligence new

✦ Visit the Claude's Cat feature page — the image, the zoom animation and Claude's Castle.

  1. Claude's Cat - Summary, A fractal cat written by an AI, and what it does and does not prove, 2026.
  2. Claude's Castle - Summary, A castle made of castles: 8 558 exact similarities, and how it differs from Claude's Cat, 2026.
  3. Claude's Cat - Full Article, A fractal cat written by an AI, and what it does and does not prove, 2026.

Book Chapters

  1. K.S. Charak & D. Rochon, On Factorization of Bicomplex Meromorphic Functions, Hypercomplex Analysis, Trends in Mathematics, Birkhäuser Verlag Basel/Switzerland, 55-68 (2008).
  2. R. Gervais Lavoie & D. Rochon, The Bicomplex Heisenberg Uncertainty Principle, Theoretical Concepts of Quantum Mechanics, ISBN 978-953-51-0088-1, InTech Book, 39-64 (2012).

Articles

  1. D. Rochon, A Generalized Mandelbrot Set for Bicomplex Numbers, Fractals, 8, No. 4, 355-368 (2000).
  2. D. Rochon, A Bloch Constant for Hyperholomorphic Functions, Complex Variables, 44, 85-101 (2001).
  3. D. Rochon, On a Generalized Fatou-Julia Theorem, Fractals, 11, No. 3, 213-219 (2003).
  4. D. Rochon, A Bicomplex Riemann Zeta Function, Tokyo Journal of Mathematics, 27, No. 2, 357-369 (2004).
  5. D. Rochon & S. Tremblay, Bicomplex Quantum Mechanics I: The Generalized Schrödinger Equation, Advances in applied Clifford algebras, 14, No. 2, 231-248 (2004).
  6. D. Rochon & M. Shapiro, On algebraic properties of bicomplex and hyperbolic numbers, Anal. Univ. Oradea, fasc. math., vol. 11 , 71-110 (2004).
  7. É. Martineau & D. Rochon, On a Bicomplex Distance Estimation for the Tetrabrot, International Journal of Bifurcation and Chaos, 15, No. 9, 3039-3050 (2005).
  8. D. Rochon & S. Tremblay, Bicomplex Quantum Mechanics II: The Hilbert Space, Advances in applied Clifford algebras, 16, No. 2, 135-157 (2006).
  9. D. Rochon, On a relation of bicomplex pseudoanalytic function theory to the complexified stationary Schrödinger equation, Complex Variables, 53, No. 6, 501-521 (2008).
  10. V. V. Kravchenko, D. Rochon & S. Tremblay, On the Klein-Gordon equation and hyperbolic pseudoanalytic function theory, J. Phys. A: Math. Theor., 41, No. 6, 1-18 (2008).
  11. K.S. Charak, D. Rochon & N. Sharma, Normal Families of Bicomplex Holomorphic Functions, Fractals, 17, No. 3, 257-268 (2009).
  12. V. Garant-Pelletier & D. Rochon, On a generalized Fatou-Julia theorem in multicomplex spaces, Fractals, 17, No. 3, 241-255 (2009).
  13. R. Gervais Lavoie, L. Marchildon & D. Rochon, The Bicomplex Quantum Harmonic Oscillator, Nuovo Cimento B, 125, No. 10, 1173-1192 (2010).
  14. R. Gervais Lavoie, L. Marchildon & D. Rochon, Infinite-Dimensional Bicomplex Hilbert Spaces, Ann. Funct. Anal, 1, No. 2, 75-91 (2010).
  15. R. Gervais Lavoie, L. Marchildon & D. Rochon, Hilbert Space of the Bicomplex Quantum Harmonic Oscillator, AIP Conference Proceedings, 1327, 148-157 (2011).
  16. R. Gervais Lavoie, L. Marchildon & D. Rochon, Finite-Dimensional Bicomplex Hilbert Spaces, Advances in applied Clifford algebras, 21, No. 3, 561-581 (2011).
  17. Rajeev Kumar, Romesh Kumar & D. Rochon, The Fundamental Theorems in the framework of Bicomplex Topological Modules, arXiv: 1109.3424 (2011).
  18. K.S. Charak, D. Rochon & N. Sharma, Normal Families of Bicomplex Meromorphic Functions, Annales Polonici Mathematici, 103, No. 3, 303-317 (2012).
  19. D. Rochon, Ravinder Kumar & K.S. Charak, Bicomplex Riesz-Fischer Theorem, GJSFR, 13-F, No. 1, 67-77 (2013).
  20. K.S. Charak, Ravinder Kumar & D. Rochon, Infinite Dimensional Bicomplex Spectral Decomposition Theorem, Advances in applied Clifford algebras, 23, No. 3, 593-605 (2013).
  21. J. Mathieu, L. Marchildon & D. Rochon, The Bicomplex Quantum Coulomb Potential Problem, Canadian Journal of Physics, 91, 1193-1100 (2013).
  22. C. Matteau & D. Rochon, The Inverse Iteration Method for Julia Sets in the 3-Dimensional Space, Chaos, Solitons & Fractals, 75, 272-280 (2015).
  23. P.-O. Parisé & D. Rochon, A Study of Dynamics of the Tricomplex Polynomial $\eta^p+c$, Nonlinear Dynamics, 82, 157-171 (2015).
  24. P.-O. Parisé, T. Ransford & D. Rochon, Tricomplex Dynamical Systems Generated by Polynomials of Even Degree, Chaotic Modeling and Simulation (CMSIM), 1, 37-48 (2017).  
  25. P.-O. Parisé & D. Rochon, Tricomplex Dynamical Systems Generated by Polynomials of Odd Degree, Fractals, 25, No. 3, 1-11 (2017).
  26. G. Brouillette, P.-O. Parisé & D. Rochon, Tricomplex Distance Estimation for Filled-in Julia Sets and Multibrot Sets, International Journal of Bifurcation and Chaos, 29, No. 6 (2019).
  27. G. Brouillette & D. Rochon, Characterization of the Principal 3D Slices Related to the Multicomplex Mandelbrot Set, Advances in applied Clifford algebras, 29, No. 39 (2019).
  28. A. Vallières & D. Rochon, Relationship between the Mandelbrot Algorithm and the Platonic Solids, Mathematics, 10, No. 482 (2022).
  29. V. Boily & D. Rochon, On the Algebraic Foundation of the Mandelbulb, Fractals, 31, No. 5 (2023).
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